Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^2$ boundedness

preprint2014arXivOpen access

We prove the $L^2$ boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.

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Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^2$ boundedness

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Hilbert transform along measurable vector fields constant on Lipschitz curves: L2L^2L2 boundedness

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Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^2$ boundedness